Diffractive electron imaging of nanoparticles on a substrate

  • A Retraction to this article was published on 01 October 2006

Abstract

There is a retraction (October 2006) associated with this Article. Please click here to view. The observation of the detailed atomic arrangement within nanostructures has previously required the use of an electron microscope for imaging. The development of diffractive (lensless) imaging in X-ray science and electron microscopy using ab initio phase retrieval provides a promising tool for nanostructural characterization. We show that it is possible experimentally to reconstruct the atomic-resolution complex image (exit-face wavefunction) of a small particle lying on a thin carbon substrate from its electron microdiffraction pattern alone. We use a modified iterative charge-flipping algorithm and an estimate of the complex substrate image is subtracted at each iteration. The diffraction pattern is recorded using a parallel beam with a diameter of 50 nm, illuminating a gold nanoparticle of 13.6 nm diameter. Prior knowledge of the boundary of the object is not required. The method has the advantage that the reconstructed exit-face wavefunction is free of the aberrations of the objective lens normally used in the microscope, whereas resolution is limited only by thermal vibration and noise.

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Figure 1: The nanodiffraction pattern of the nanostructure under study.
Figure 2: A typical reconstructed image.
Figure 3: The residual R factor as a function of iteration number.
Figure 4: The reconstructed exit-face wavefunction of the nanogold ball.
Figure 5

References

  1. 1

    Chapman, H. N. et al. High-resolution ab initio three-dimensional X-ray diffraction microscopy. J. Opt. Soc. Am. A (in the press).

  2. 2

    Zuo, J. M., Vartanyants, I., Gao, M., Zhang, R. & Nagahara, L. A. Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419–1421 (2003).

  3. 3

    Shapiro, D. et al. Biological imaging by soft x-ray diffraction microscopy. Proc. Natl Acad. Sci. USA 102, 15343–15346 (2005).

  4. 4

    McMahon, P. J. et al. Quantitative phase radiography with polychromatic neutrons. Phys. Rev. Lett. 91, 145502 (2003).

  5. 5

    Scherzer, O. The theoretical resolution limit of the electron microscope. J. Appl. Phys. 20, 20–29 (1949).

  6. 6

    Coene, W., Janssen, G., Op de Beeck, M. & Van Dyck, D. Phase retrieval through Focus variation for ultra-resolution in field-emission transmission electron microscopy. Phys. Rev. Lett. 69, 3743–3746 (1992).

  7. 7

    Haider, M., Uhlemann, S., Schwan, E., Kabius, B. & Urban, K. Electron microscope image enhanced. Nature 392, 768–769 (1998).

  8. 8

    Spence, J. C. H. Oxygen in crystals—seeing is believing. Science 299, 839–840 (2003).

  9. 9

    Jia, C. L., Lentzen, M. & Urban, K. Atomic-resolution imaging of oxygen in perovskite ceramics. Science 299, 870–873 (2003).

  10. 10

    Orchowski, A., Rau, W. D. & Lichte, H. Electron holography surmounts resolution limit of electron microscopy. Phys. Rev. Lett. 74, 399–402 (1995).

  11. 11

    Glaeser, R. Review: Electron crystallography: present excitement, a nod to the past, anticipating the future. J. Struct. Biol. 128, 3–14 (1999).

  12. 12

    Miao, J. W., Charalambous, C., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).

  13. 13

    Gerchberg, R. W. & Saxton, W. O. Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972).

  14. 14

    Fienup, J. R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).

  15. 15

    Oszlányi, G. & Sütő, A. Ab initio structure solution by charge flipping. Acta Crystallogr. A 60, 134–141 (2004).

  16. 16

    Wu, J. S., Spence, J. C. H., O’Keeffe, M. & Groy, T. Application of a modified Oszlányi and Süto ab initio charge-flipping algorithm to experimental data. Acta Crystallogr. A 60, 326–330 (2004).

  17. 17

    Wu, J. S., Weierstall, U., Spence, J. C. H. & Koch, C. T. Iterative phase retrieval without support. Opt. Lett. 29, 2737–2739 (2004).

  18. 18

    Spence, J. C. H. High-resolution Electron Microscopy (Oxford Univ. Press, Oxford and New York, 2003).

  19. 19

    Spence, J. C. H., Weierstall, U. & Howells, M. Coherence and sampling requirements for diffractive imaging. Ultramicroscopy 101, 149–152 (2004).

  20. 20

    Wu, J. S. & Spence, J. C. H. Reconstruction of complex single-particle images using the charge-flipping algorithm. Acta Crystallogr. A 61, 194–200 (2005).

  21. 21

    Marchesini, S. et al. X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003).

  22. 22

    Oszlányi, G. & Sütő, A. Ab initio structure solution by charge flipping II. Use of weak reflections. Acta Crystallogr. A 61, 147–152 (2005).

  23. 23

    Seldin, J. & Fienup, J. R. Numerical investigations of the uniqueness of phase retrieval. J. Opt. Soc. Am. 7, 412–427 (1990).

  24. 24

    Buerger, M. J. Proofs and generalizations of pattersons theorems on homometric complementary sets. Z. Kristallogr. 143, 79–98 (1976).

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Acknowledgements

This work was supported by ARO award W911NF-05-1-0152 and a UK EPSRC award.

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Correspondence to Jinsong Wu.

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The authors declare no competing financial interests.

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Wu, J., Weierstall, U. & Spence, J. Diffractive electron imaging of nanoparticles on a substrate. Nature Mater 4, 912–916 (2005). https://doi.org/10.1038/nmat1531

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